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Find the solution of the system of equations. {:[3x+7y=-2],[4x-7y=-19]:} (_________,________)

Find the solution of the system of equations.\newline3x+7y=−24x−7y=−19 \begin{array}{l} 3 x+7 y=-2 \\ 4 x-7 y=-19 \end{array} \newline(_________,________)

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Full solution

Q. Find the solution of the system of equations.\newline3x+7y=−24x−7y=−19 \begin{array}{l} 3 x+7 y=-2 \\ 4 x-7 y=-19 \end{array} \newline(_________,________)
  1. Add Equations Together: Add the two equations together to eliminate yy.(3x+7y)+(4x−7y)=−2+(−19)(3x + 7y) + (4x - 7y) = -2 + (-19)7x=−217x = -21
  2. Divide to Solve xx: Divide both sides by 77 to solve for xx.7x7=−217\frac{7x}{7} = \frac{-21}{7}x=−3x = -3
  3. Substitute xx in First Equation: Substitute x=−3x = -3 into the first equation to solve for yy.3(−3)+7y=−23(-3) + 7y = -2−9+7y=−2-9 + 7y = -2
  4. Isolate 7y7y Term: Add 99 to both sides to isolate the 7y7y term.\newline7y=−2+97y = -2 + 9\newline7y=77y = 7
  5. Divide to Solve yy: Divide both sides by 77 to solve for yy.7y7=77\frac{7y}{7} = \frac{7}{7}y=1y = 1

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